All Questions
10
questions
0
votes
1
answer
53
views
Optimal Card Game Schedule
I have the responsibility of creating a schedule for a card game league. While creating the schedule, the following problem has arisen...
Let $n,g,s \in \mathbb{N+}$ where $s \leq n$.
Let $P = \{1, 2, ...
- 213
3
votes
1
answer
410
views
How to find a set of combinations of 5 that cover all the combinations of 3 once?
I have a set of n numbers (e.g. 1 to n). For the sake of clarity, in the remaining I will use n = 10.
From these 10 numbers there is $\binom{10}{3} = 120$ combinations of 3, for instance (1, 3, 5), (3,...
- 33
2
votes
0
answers
50
views
Enumerating separating subcollections of a set
Let $S$ be a (finite) set, and let $C \subseteq 2^S$ be a collection of subsets of $S$. We say that a subcollection $C' \subseteq C$ is separating if for any two elements of $S$ there exists a subset ...
- 11.2k
0
votes
1
answer
83
views
Finding sets that satisfy intersection cardinalities
Let's say I have a set of elements $V$. I can use all subsets of $V$ of size $k$ to satisfy intersection conditions.
Example:
$V = \{ 1, 2, 3, 4, 5\}$, $k = 3$.
$|B_1 \cap B_2|=2$,$|B_2 \cap B_3|=2$,$|...
- 295
4
votes
1
answer
515
views
Collection of subset generating every pairs of elements
I'm looking forward to a construction with the following property:
Given a set S of n elements, find a small/the smallest collection of subsets of S of size k such that for every pair of elements a, ...
- 51
5
votes
0
answers
80
views
Arranging playdate groups
At my kids' school, the kids are meeting in playdate groups of two girls and two boys every month. The groups are constructed to get as much variation in the groups over the months. Having seen too ...
2
votes
2
answers
688
views
Combining kindergardeners in 'fair' cookie-baking groups. Kirkman's schoolgirl problem extended version
I am coordinating cookie-baking events with kindergarten kids. This turns out to be a challenging problem, and I could use a little help:
We would like a general way of creating 'fair' cookie-baking ...
- 123
4
votes
0
answers
95
views
partitions of finite set in same-size parts having at most one element in common
Given $g \ge 2$, $k \ge 1$ and a population of $p = kg$ workers, I'm trying to figure out the longest series of work shifts such that:
during each shift, all workers work in $k$ teams of g people;
...
- 257
2
votes
2
answers
2k
views
What algorithm is a good to search a lotto design?
I'm interested what kind of algorithm would be suitable to find a lotto design? I saw that is has been proven that $L(39,7,4,7)=329$. This notation is explained in http://web.archive.org/web/...
- 21
5
votes
1
answer
957
views
A generalization of Kirkman's schoolgirl problem
A friend of mine asked me this question. "I have $3n$ elements, and I want to know which is the maximum number of triplets $(a,b,c)$ so that no two triplets have more than one element in common".
The ...
- 9,944